The present invention is concerned with a fuel cell and in particular with a fuel cell which provides increased operating efficiency by maximising the available interfacial area between high and low density fluid phases or between gas-liquid-solid phases, across which phases heat and mass transfer and chemical reactions may take place. The present invention also provides for a novel method of improving the efficiency and performance of fuel cells by subjecting them to forced rotation.
Fuel cells are devices for utilizing the electrochemical conversion of the free-energy changes of a chemical reaction directly into electrical energy. By making use of gaseous or solid reactants (e.g. hydrogen, oxygen, or metallic powders) the anodic and cathodic reactants can be fed into their respective chambers where the electrochemical energy conversion proceeds. An electrolyte layer (often a liquid) is provided between the two electrodes of an electrochemical cell. At the anode, the half-cell reaction involving the anodic reagent yields electrons which are transported through an external circuit to the cathode where they are taken up in the half-cell reaction involving the cathodic reactant, usually oxygen. The circuit is completed by the transport of ions from one electrode to the other through the electrolyte, Current passing through the external electrical circuit provides electrical power and allows mechanical work to be done via, for example, an electric motor.
Unlike batteries which store electrical energy, fuel cells are energy producers which convert the energy of chemical reactions directly into electricity. They do so in an environmentally clean way, with no harmful pollutants such as those which arise from the normal burning of fuels in conventional combustion processes. Because fuel cells are not limited to the thermodynamic (Carnot) efficiencies of internal combustion engines (typically 40-50%), they offer much greater prospects for achieving high efficiencies (70-100%) and energy conversion rates. In order to attain these high efficiencies, however, new designs of compact fuel cells are required which can extract the electrochemical energy in a more effective manner. Achievable power output and performance is limited by the slow diffusion of ions and electrons at the reactant-electrolyte-electrode interface, especially in the case where the reactant is a gas.
Fuel cells are often classified according to their basic system configuration. The most common classifications include: phosphoric acid fuel cells (PAFCs); molten carbonate fuel cells (MCFCs); solid oxide fuel cells (SOFCs); proton exchange membrane fuel cells (PEMFCs); alkaline fuel cells (AFCs); and direct methanol fuel cells (DMFCs). In another classification, fuel cell types are grouped according to the fuel and oxidant consumed, e.g. hydrogen-oxygen (or air) fuel cells; organic compounds-oxygen (or air) fuel cells; carbon or carbon monoxide-oxygen (or air) fuel cells; nitrogenous compounds-oxygen (or air) fuel cells; and metal-oxygen (or air) fuel cells. Conventional fuel cells are typically composite quasi-static structures incorporating numerous individual electrochemical cells stacked in series and parallel to generate the required output voltage and current density. The present invention is particularly suited to the metal-oxygen type of fuel cell, and also the hydrogen-oxygen type of fuel cell, but is not exclusively limited to them.
One objective of the present invention is therefore to provide a fuel cell with increased working efficiency which alleviates to some extent problems associated with previously used fuel cells.
Accordingly, the present invention provides for a fuel cell comprising:
a chamber suitable for holding an electrolyte therein;
a mechanism which enables rotation of the electrolyte about an axis of rotation of the chamber;
one or more structures which define one or more inlets for introducing an oxidant and/or a fuel into the chamber, which one or more inlets are spaced from the axis of rotation of the chamber;
at least one electrode contactable with the electrolyte and the oxidant; and
at least one electrode contactable with the electrolyte and the fuel;
Fuel cells currently known in the art frequently employ a liquid electrolyte and a gaseous oxidant (e.g. air or oxygen) and/or fuel (e.g. hydrogen). The circulation of the gaseous oxidant and/or fuel through the electrolyte relies upon buoyancy-driven natural convection processes. In all buoyancy-driven natural convection processes on earth, the driving forces arise through the interaction of matter with the earth""s gravitational field. The xe2x80x98rise velocityxe2x80x99, i.e. the natural velocity attained by the lighter phase, such as a bubble of gas, with respect to the heavier phase, usually a liquid, is therefore governed by the value of the local gravitational acceleration, which on earth is roughly constant at 9.81 m/s2. This rise velocity can be increased substantially by intensifying the local acceleration field using rotating frames such as centrifuges or other spinning devices.
In the fuel cell of the present invention, centrifugal forces acting on the electrolyte phase, together with inverse-centrifugal (centripetal) forces acting on the oxidant and/or fuel phases, act jointly to increase the overall circulation flow rate. When the induced inertial acceleration exceeds that of the normal local gravitational field, this externally-forced flow process may promote an increase in volumetric throughput of chemical substances in a reactor and hence improve the overall rate of chemical reaction. In ordinary xe2x80x98staticxe2x80x99 fuel cells, the overall rate of chemical reaction and therefore the overall power density achievable from the device may be limited by the local gravitational field. In the fuel cell of the present invention the improved overall rate of chemical reaction will increase the power density achievable from the device.
Advantageously, the acceleration field induced in the fuel cell of the present invention as a result of rotation of the electrolyte about an axis of rotation of the chamber and the improved convection which results can also promote and enhance the internal circulation of the electrolyte fluid without the use of pumps. Under strong rotation, when the angular velocity is sufficiently high to induce a local linear acceleration substantially greater than the normal local gravitational field (approximately 9.81 m/s2), this flow process is referred to as xe2x80x98enhanced natural circulationxe2x80x99. The present invention thus advantageously utilises enhanced natural circulation to provide an increase in the power output of fuel cells, such as for example metal-oxygen (or air) fuel cells.
The increase in the bubble rise velocity also brings with it concomitant increases in the throughput of chemical substances which can substantially improve the yield from an electrochemical reaction process. This is particularly advantageous because, generally, the performance of conventional electrochemical reactors is limited by the maximum achievable flow rate of oxidant and/or fuel, which are usually gases, passing through a porous electrode in an electrolyte (usually a liquid), and the available interfacial area between the different phases across which heat and mass transfer and electrochemical reactions take place.
It will be appreciated by those skilled in the art that the rotation of the electrolyte about an axis of symmetry of said chamber may be achieved in a number of ways. However, preferably, the mechanism which enables rotation of said electrolyte comprises a mechanism which enables rotation of said chamber. Obviously, rotating the chamber containing the electrolyte automatically rotates the electrolyte itself. This may, for example, be achieved by means of an electric motor. Thus, the reactor may, in one embodiment, comprise a centrifuge or the like.
The chamber may, in another embodiment, be rotated by providing a plurality of guide vanes and/or impellers thereon, which cause said chamber to rotate upon introduction of the oxidant and/or fuel into the fuel cell. In this embodiment of the invention, the impellers/guide vanes may be provided outside said chamber, which itself may be provided inside an external housing. Thus, advantageously, introduction of the oxidant and/or fuel into the external housing imparts movement to the chamber by impinging on said guide vanes prior to its introduction into the chamber for reaction. Thus, an external rotation mechanism, such as an electric motor or the like, may not be required, the rotation being induced primarily by the pressure and momentum change of the introduced oxidant and/or fuel impinging on said guide vanes to impart movement to the chamber.
Alternatively, the mechanism which enables rotation of the electrolyte may comprise rotating impellers or baffles or the like provided within said chamber.
When the electrolyte is rotated about an axis of rotation of the chamber, centrifugal and Coriolis forces serve to increase the buoyancy forces on the oxidant and/or fuel entering the fuel cell through the inlet for introducing oxidant and/or fuel into said chamber. The fuel cell thus works on an xe2x80x98inverse centrifugexe2x80x99 type principle. The xe2x80x98inverse centrifugexe2x80x99 principle provides the action by which a continuous flow of a lower density fluid through another higher density fluid can be maintained, the induced buoyancy forces being caused by centripetal forces acting on the lighter phase.
Fuel cells which rely on a continuous recirculation of liquid electrolyte could benefit from the xe2x80x98inverse centrifugexe2x80x99 effect. For example a gas, which ray constitute either the fuel and/or the oxidant, introduced. Into the electrolyte will reduce the local fluid density and this density reduction can be used to drive a continuous xe2x80x98enhanced natural circulationxe2x80x99 around the fuel cell. This circulating flow is increased in direct proportion to the increase in acceleration field resulting from an increase in angular velocity or spin speed of the electrolyte about the axis of rotation. Further, the xe2x80x98bubbling actionxe2x80x99 of the gas can substantially increase the electrochemical reaction rate by increasing the gas-liquid-solid interfacial area at the reaction sites. The fuel and/or oxidant gases may be supplied under pressure through the one or more inlets located away from the axis of rotation. Preferably, the one or more inlets are provided in the peripheral walls of said chamber which are furthest from the axis of rotation. The rates of heat and mass transfer are also increased. Rotation therefore serves to promote and increase the continuous natural circulation of the electrolyte and to promote and increase the throughput of oxidant and/or fuel in a fuel cell in a manner analogous to the flow in a centrifugal bubble column or disk, without the use of pumps. The exploitation of xe2x80x98enhanced natural circulationxe2x80x99 by the fuel cell of the present invention reduces the need for external pumps, piping or other components which are ordinarily required for the circulation of the electrolyte within the fuel cell. This results in a more compact and cost-effective design with substantially fewer moving parts, thus increasing overall reliability. The enhanced throughput of oxidant and/or fuel also enables the use of higher flow resistance (and hence denser) electrodes, in turn contributing to a higher energy yield. As well as enhancing ionic transport between the electrodes the enhanced natural circulation of the electrolyte also reduces the dendritic growth of species such as metal oxide crystals which can be responsible for short circuiting fuel cell devices.
Another advantage of the fuel cell of the present invention is the controllability of its power output. This may be achieved by variation of the spin speed of the electrolyte. Increasing the spin speed increases the throughput of reactants thus increasing the rate of reaction. This improves the uniformity of power generation.
The incorporation of a spin-axis is also a useful engineering feature. Having a single common axis of rotation, a fully integrated xe2x80x98stand alonexe2x80x99 power unit can be designed having the fuel cell reaction chamber, oxidant and/or fuel delivery system, exhaust discharge systems, electric drive motor and spin-speed regulator all on one shaft. Direct coupling to an inertial flywheel or drive/transmission system is also possible. For applications in space where earth-derived gravitational forces are practically absent, the creation of artificial gravity by spinning centrifuges may be the only means of achieving induced natural convection flow processes.
Optionally, the fuel cell may also provide at least one structure defining at least one outlet for removal of said oxidant and/or said fuel adjacent said axis of rotation.
Preferably, when one or more outlets are present, the inlet(s) and outlet(s) are located at opposite ends of the chamber. This advantageously provides the maximum interfacial area between the electrodes and the oxidant and/or fuel for electrochemical reactions to occur.
Preferably, introduction of the oxidant and/or fuel into the chamber and subsequently into contact with said electrolyte and said electrodes may be by way of sparging means. This, advantageously, provides a plurality of inlets which deliver the oxidant and/or fuel and optimises the reactive surface area in the chamber. Advantageously, when a gas is used as the oxidant and/or fuel, the sparging means delivers bubbles of a uniform size.
Preferably, the fuel cell also comprises one or more compressors which pressurise the oxidant and/or fuel prior to introduction into the fuel cell via the one or more inlets for the oxidant and/or fuel. Preferably the compressor is driven using energy supplied by the fuel cell
Preferably, the fuel cell also comprises one or more low-pressure turbines which de-pressurise any oxidant and/or fuel leaving the fuel cell via the one or more outlets for the oxidant and/or fuel. The recovered energy can be redirected back to other components of the fuel cell such as the compressor or the mechanism which enables rotation of the electrolyte. This improves the energy efficiency of the device.
Preferably the fuel cell also comprises a feedback mechanism which regulates the flow of oxidant and/or fuel through the fuel cell so as to minimise any undesirable vibrations which may occur due to nonuniform distribution of oxidant and/or fuel.
Preferably, the electrodes comprise porous electrically conductive material. Preferably, the electrodes comprise three-dimensional blocks rather than two-dimensional plates. In a metal-oxygen (or air) fuel cell, the metal fuel is itself the electrode which contacts the oxidant. That is to say, the metal acts both as oxidant and electrode. The meal fuel may be fabricated in the form of a solid porous block or supplied as a loosely compacted metal powder retained within a porous metal cage watch cage acts as an electrical contact as well as providing structural support. The electrode which contacts the oxidant preferably comprises a porous electrically-conducting solid material such as porous sodium-tungsten-bronze or a porous carbon material such as pyrolized porphyrins.
A fuel cell wherein the fuel is a metal and the oxidant is oxygen or air represents a preferred embodiment of the present inventions. In this case, the metal fuel may be provided in the form of a powder for continuous feeding or as a single xe2x80x98chargexe2x80x99 of compacted porous metal. The electropositive metals most suitable for metal-oxygen fuel cells include, in order of decreasing electrochemical energy equivalent: lithium, aluminium, magnesium, calcium, iron and zinc. Aluminium is second only to lithium in terms of gravimetric energy density but is superior on volumetric grounds and is also cheaper and less toxic. Thus aluminium is preferred as the metal fuel.
When the fuel used is a metal the chamber advantageously additionally comprises a porous cage for containing said metal. In this type of fuel cell, the electrolyte preferably comprises hydroxide ions, more preferably, said electrolyte comprises an aqueous solution of potassium or sodium hydroxide.
In a particularly preferred embodiment of the present invention the chamber additionally comprises internal baffles which separate the oxidant electrode and the fuel electrode and which define passageways for the internal recirculation of the electrolyte.
Even more preferably the chamber may additionally comprise a trap for the collection and/or removal of reaction products from the cell. For a fuel cell wherein the fuel is a metal and the oxidant is oxygen or air, the trap may comprise a chemical precipitate trap (such as calcium oxide) which retains the reaction by-product (such as metal hydroxide).
In a preferred embodiment of the present invention the chamber may be subdivided into smaller chambers to create a plurality of electrochemical cells spaced around the circumference of the chamber which may be electrically connected to each other in series or in parallel
Preferably, the speed of rotation of the electrolyte may be variable. That is to say, the mechanism which enables rotation of the electrolyte may provide for rotation at variable speed. More preferably, the rotation may driven by an external mechanism such as an electric motor which may be integral with the fuel cell. The electric motor which drives rotation may be powered by electricity generated by the fuel cell itself. A particularly preferred embodiment is a xe2x80x98self-startingxe2x80x99 cell wherein the fuel cell remains operative even when it is not spinning so that it may provide sufficient electrical power to start-up the electric motor.
Preferably, the electrolyte may be rotated with its spin axis oriented in the vertical direction.
In a further aspect of the invention there may also be provided a fuel cell system comprising a plurality of fuel cells according to the present invention which fuel cells are physically connected in series with one another and electrically connected in series or in parallel with one another. The electrical connections allow the electrical characteristics of the system to be varied. In a preferred embodiment of the fuel cell system the fuel cells are all mounted on a common spin axis.
The present invention also encompasses within its scope a vehicle comprising a fuel cell or a fuel system as herein described.
According to a further aspect of the present invention there is provided a method for improving the efficiency and performance of fuel cells which method comprises introducing an oxidant and/or fuel into contact with an electrolyte present in a fuel cell as defined herein by means of the one or more inlets spaced from the axis of rotation of said chamber and rotating the electrolyte about the axis of rotation of said chamber. Any unreacted oxidant and/or unreacted fuel may be optionally removed by means of one or more outlets adjacent said axis of rotation.
Preferably, the electrolyte in said chamber is rotated by rotating said chamber. The chamber may be rotated by external means (e.g. an electric motor) or alternatively by providing guide vanes or baffles on said chamber which cause said chamber to rotate upon introduction of said oxidant and/or fuel into said fuel cell.
The method of the present invention may further comprise allowing solvent (usually water) to boil off from the electrolyte. This is advantageous because it helps to maintain the correct electrolyte concentrations and pH within the fuel cell. It also helps to dissipate internal heat generation caused by ohmic resistance and 12R losses.
The method of the present invention may further comprise the step of regenerating the parent chemical fuel and oxidant from the reaction by-products.
Apart from the usual benefits claimed for all fuel cells, such as clean electrochemical xe2x80x98combustionxe2x80x99 with no harmful emissions to the atmosphere, the additional advantages claimed of this invention are basically threefold. (i) The centrifuge action serves to increase the operating pressure within the fuel cell without increasing the temperature. The reasons why the electrical output is thereby increased may be attributable to the increase in interfacial contact area between the oxidant and/or fuel and electrolyte at the reaction site within the pores of the electrode, directly influencing the ion exchange process. (ii) Intensification of the acceleration field induced by rotation can be used to increase the throughput of fuel and/or oxidant by the inward centripetal force acting on the low density phase (i.e. the oxidant and/or fuel), and the outward centrifugal force acting on the high density phase (i.e. the electrolyte), thereby increasing the oxidant and/or fuel diffusion rate and hence the overall reaction rate and power output. (iii) The rotation can be readily sustained by a small electric motor deriving energy from the fuel cell itself and mounted on the common spin axis. Excess electrical power or rotational kinetic energy could then be utilized for mechanical traction in automotive applications by direct drive electric motors, possibly incorporating energy storage techniques (e.g. flywheels or batteries).
In a typical hydrogen-oxygen fuel cell, gaseous fuel and oxidant are pumped separately under pressure through porcus electrodes in contact with an electrolyte. Pressurisation permits them to operate in zero-gravity conditions as well as on earth. However, a rotating fuel cell offers advantages not achievable in a solely static pressurised system. These benefits derive not only from the accompanying increase in pressure. Through the xe2x80x98inverse-centrifugexe2x80x99 effect, the increased buoyancy forces dynamically stimulate the process of oxidant/electrolyte and/or fuel/electrolyte mixing and diffusion, thereby enhancing the chemical reaction process. Increasing the local acceleration field (by rotation) has a very strong influence on buoyancy, on the dynamics of bubble motion and the bubble xe2x80x98rise velocityxe2x80x99. A rotating fuel cell can therefore take advantage of dynamic effects not present in conventional static pressurised fuel cells.
As previously mentioned, a particularly preferred embodiment of the invention comprises a fuel cell for xe2x80x98burningxe2x80x99 metallic fuel (e.g. powdered aluminium or zinc) comprising porous matrix xe2x80x98oxygenxe2x80x99 electrodes within a liquid electrolyte. Such a fuel cell can also benefit substantially from centrifugal effects when constructed as a rotating fuel cell. The additional advantages over conventional static metal-oxygen fuel cell designs are as follows. (i) The oxidizing gas (oxygen or air) injected into the porous matrix oxygen electrode, by virtue of the intense xe2x80x98bubbling actionxe2x80x99, can significantly increase the reaction rate by creating a pulsating gas-liquid film at the xe2x80x98three-phase boundaryxe2x80x99 within the oxygen electrode. Rapid random movements of this localized wetted film region promotes a significant increase in charge transfer at the gas-liquid-solid interface. (ii) The rising gas stream reduces the average fluid density in the electrolyte surrounding the oxygen electrode, which, together with the increased centrifugal force due to rotation of the liquid in the fuel chamber, promotes enhanced natural circulation of electrolyte around the cell. (iii) Oxygen or air not consumed in the reduction process is readily discharged from the fuel cell by means of improved gas-liquid separation at the electrolyte free surface assisted by the rotational centrifuge effects. (iv) Reactant by-products can be effectively xe2x80x98trappedxe2x80x99 away from the axis of rotation by centrifugal forces without impeding the flow of electrolyte around the cell. These chemical by-products can either be continuously (or intermittently) removed, or, in a closed loop system, regenerated to yield the parent metal fuel plus oxygen for subsequent re-use. (v) Centrifugal forces can be utilized to an advantage as a means of feeding the cell with fresh metallic fuel. These xe2x80x98outwardxe2x80x99 centrifugal forces can be used to distribute and compact the powdered fuel, simplifying the design of the fuel supply system. (vi) A xe2x80x98fluidized bedxe2x80x99 of fuel particles can be maintained to yield a large increase in interfacial area between the fuel and electrolyte. This improves overall fuel cell performance and efficiency by augmenting the electrochemical reaction rate. (vii) Powdered aluminium is particularly preferred because it is readily obtainable in a very pure condition at low cost. Being strongly electropositive, it therefore provides a suitably cheap fuel which can be electrochemically xe2x80x98burnedxe2x80x99 without the release of noxious gases. The system is also chemically regenerative with a low cost of regeneration. (viii) The compactness of the metal fuel together with the low temperature of operation result in fewer material problems, higher reliability and longer life for the cell. A spinning configuration also provides for a smaller overall design, hence reduced mass and increased power-to-weight ratio.
Depending on the specific type, a rotating fuel cell could be engineered in many different ways especially with regard to te geometry of the gas and liquid flow paths, electrode configuration, design of electrolyte chambers and the mechanical/electrical connections between individual cells. One feature which will generally he common to rotating fuel cells however is that the injected oxidant and/or fuel are introduced at those regions corresponding to substantially the outer-most radius of the particular electrochemical cell. Thus, the typical back-to-back arrangement of electrodes in conventional fuel cells should instead be redesigned to facilitate the centrifuge-enhanced diffusion of gases through the electrolyte-wetted regions of the electrodes. For any given cell, the two electrodes could for example be opened out edge-to-edge fashion, preferably, but not necessarily, on a plane of constant radius.
One possible back-to-back configuration for a fuel cell utilising spin-enhanced natural circulation would be to spatially separate the xe2x80x98fuel electrodexe2x80x99 from the xe2x80x98oxidant electrodexe2x80x99 by a common radial channel or conduit in such a way as to permit a double-loop recirculation of the electrolyte. Gaseous fuel such as hydrogen may be injected by means of a sparger into the outer Periphery of the fuel electrode Likewise, gaseous oxidant such as air may be injected separately into the outer periphery of the oxidant electrode. Liquid electrolyte could then circulate freely by flowing radially outwards in the common central channel from where it would divide to flow into the two sparger regions of the fuel and oxidant inlets. The radial inward flow of gases, and the resulting reduction in two-phase mixture densities in the separated fuel and oxidant sections will promote enhanced circulation of liquid electrolyte around the fuel cell. Further requirements to balance gas and electrolyte pressures in order to control the position of the wetted interface within the electrodes may be achieved by pressure regulation or through control of rotational spin speed.
Electrode design in metal-oxygen fuel cells is somewhat less complex and, therefore, allows better use of the inverse-centrifuge principle to control the gas and liquid flows through the porous structures of the two electrodes.
In some fuel cell designs, the electrolyte, which may be an acid or alkaline aqueous solution, continuously circulates between the electrodes. As stated already, in a rotating fuel cell, centrifugal forces causes a large increase in hydrostatic pressure in the electrolyte which, up to a limit, is beneficial to fuel cell operation and performance. By injecting gas (fuel or oxidant) under pressure through small nozzles at the outer periphery of the centrifuge chamber, a drastic reduction in density of the gas-liquid mixture is produced which promotes enhanced natural circulation of the liquid electrolyte around the cell. The pressure and circulation flow rate can both be directly augmented by simply increasing the rotation speed.
The advantages of rotation outweigh the additional complexity of driving the rotation by, for example, an electric motor. Useful advantages arise from the coupling of the hydrodynamic and electrochemical processes which together increase the overall efficiency and specific power output from such a device. Rotation can be used to set up and control an enhanced convection-type flow of the gas-liquid two-phase mixture forming the recirculating electrolyte. This avoids the need for pumps to force the liquid around the fuel cell circuit, thus eliminating ancillary control circuits and reducing material corrosion problems. Further, the pressure within the fuel cell can be increased to optimize the electrochemical reaction rates at the electrode surfaces by controlling spin speed By injecting gas (e.g. hydrogen, oxygen or air) directly into the electrode, the resultant xe2x80x98bubblingxe2x80x99 action brings about localized random movements of the electrolyte film at the gas-liquid-solid interface which increases the electrochemical reaction rate. This is known to greatly improve the exchange of electronic and ionic charge at the xe2x80x98three-phase boundaryxe2x80x99 and can produce a 100-fold increase in current density at the electrode. A very large increase in interfacial area between a solid fuel (e.g. powdered aluminium) and the liquid electrolyte can advantageously be sustained by xe2x80x98fluidizingxe2x80x99 the solid particles. Producing a xe2x80x98fluidized bedxe2x80x99 makes the metallic fuel particles dynamically buoyant, increasing the interfacial contact area and thus the electrical power density obtainable from a given quantity of fuel.
Further advantages of a rotating fuel cell stem from the typically intermittent nature of power sources needed for domestic transportation purposes. For these applications, the means of rotation may be derived via the main transmission system whilst consuming only a small fraction of the total power produced. The additional power required for maintaining this rotation is low compared to the overall power needed for vehicle acceleration. This additional power will be used mainly to overcome frictional resistance in bearings and to compress the oxidant gas (e.g. air) for pressurised operation. Such a drive mechanism could be geared into the main transmission system for road vehicles and coupled to total power demand. In this way, fuel cell spin rate could be geared to road speed, possibly utilizing a flywheel effect to manage and control spin velocity and thereby generate higher specific power on demand for an increase in acceleration.